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A228287
Smallest value of z in the minimal value of x + y*z, given x + y*z = n (where x, y, z are positive integers).
3
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1
OFFSET
2,7
COMMENTS
If there are multiple triples (x, y, z) for which xy + z = n and x + yz is minimized, consider the triple with smallest z. I.e., this sequence illustrates the smallest z needed to minimize x + yz.
For n = 215 the triples (53, 4, 3) and (35, 6, 5) both give the minimal value of x + yz = 65. Thus a(215) = 3.
MAPLE
A228287 := proc(n)
local a, x, y, z, zfin ;
a := n+n^2 ;
zfin := n ;
for z from 1 to n-1 do
for x in numtheory[divisors](n-z) do
y := (n-z)/x ;
if x+y*z < a then
a := x+y*z ;
zfin := z ;
end if;
end do:
end do:
return zfin;
end proc: # R. J. Mathar, Sep 02 2013
MATHEMATICA
A228287[n_] := Module[{a, x, y, z, zfin}, a = n + n^2; zfin = n; Do[Do[y = (n-z)/x; If[x + y*z < a, a = x + y*z; zfin = z], {x, Divisors[n-z]}], {z, 1, n-1}]; zfin];
Table[A228287[n], {n, 2, 100}] (* Jean-François Alcover, Aug 08 2023, after R. J. Mathar *)
CROSSREFS
Cf. A228286.
Sequence in context: A307614 A363057 A242481 * A213636 A192393 A184303
KEYWORD
nonn
AUTHOR
Andy Niedermaier, Aug 19 2013
STATUS
approved